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arXiv · 1011.1001

Colourings of lattices and coincidence site lattices

Manuel Joseph C. Loquias·Peter Zeiner
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Abstract

The relationship between the coincidence indices of a lattice $Γ_1$ and a sublattice $Γ_2$ of $Γ_1$ is examined via the colouring of $Γ_1$ that is obtained by assigning a unique colour to each coset of $Γ_2$. In addition, the idea of colour symmetry, originally defined for symmetries of lattices, is extended to coincidence isometries of lattices. An example involving the Ammann-Beenker tiling is provided to illustrate the results in the quasicrystal setting.

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Manuel Joseph C. Loquias, Peter Zeiner. 2010-11-03. Colourings of lattices and coincidence site lattices. https://doi.org/10.1080/14786435.2010.524900

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